Question

Find the equation of the line with the given properties. Passes through (4, -5) with a slope of -1\2

Answer 1

`y=-(1)/(2)x-3`

Step-by-step explanation

when you know the slope and a passing point of the line, you can find the equation of the line by replacing in the slope-point equation ,it is given by:

`\begin{gathered} y-y_1=m(x-x_1) \\ \text{where } \\ m\text{ is the slope} \\ \text{and} \\ (x_1,y_1)\text{ is a point from the line } \end{gathered}`

then

Step 1

a)Let

`\begin{gathered} \text{slope}=-(1)/(2) \\ \text{ Point=(4,-5)} \end{gathered}`

now,replace and solve for y

`\begin{gathered} y-y_1=m(x-x_1) \\ y-(-5)=-(1)/(2)(x-4) \\ y+5=-(1)/(2)x+(4)/(2) \\ y+5=-(1)/(2)x+2 \\ \text{subtract 5 in both sides} \\ y+5-5=-(1)/(2)x+2-5 \\ y=-(1)/(2)x-3 \end{gathered}`

therefore, the answer is

`y=-(1)/(2)x-3`

I hope this helps you